An application of a theorem of alternatives to origami

Abstract

Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R2. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale's theorem of alternatives is useful for the study of twist fold.

abstract = "Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R2. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale's theorem of alternatives is useful for the study of twist fold.",

author = "Hidefumi Kawasaki",

year = "2017",

month = "7",

day = "1",

doi = "10.15807/jorsj.60.393",

language = "English",

volume = "60",

pages = "393--399",

journal = "Journal of the Operations Research Society of Japan",

issn = "0453-4514",

publisher = "Operations Research Society of Japan",

number = "3",

}

TY - JOUR

T1 - An application of a theorem of alternatives to origami

AU - Kawasaki, Hidefumi

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R2. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale's theorem of alternatives is useful for the study of twist fold.

AB - Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R2. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale's theorem of alternatives is useful for the study of twist fold.